Theoretical models of psychotherapy not only try to predict outcome but also intend to explain patterns of change. Studies showed that psychotherapeutic change processes are characterized by nonlinearity, complexity, and discontinuous transitions. By this, theoretical models of psychotherapy should be able to reproduce these dynamic features. Using time series derived from daily measures through internet-based real-time monitoring as empirical reference, we earlier presented a model of psy- chotherapy which includes ﬁve state variables and four trait variables. In mathematical terms, the traits modulate the shape of the functions which deﬁne the nonlinear interactions between the variables (states) of the model. The functions are integrated into ﬁve coupled nonlinear difference equations. In the present paper, we model how traits (dispositions or competencies of a person) can continuously be altered by new experiences and states (cognition, emotion, behavior). Adding equations that link states to traits, this model not only describes how therapeutic interventions modulate short-term change and ﬂuctuations of psychological states, but also how these can inﬂuence traits. Speaking in terms of Synergetics (theory of self-organization in complex systems), the states correspond to the order parameters and the traits to the control parameters of the system. In terms of psychology, trait dynamics is driven by the states—i.e., by the concrete experiences of a client—and creates a process of personality development at a slower time scale than that of the state dynamics (separation of time scales between control and order parameter dynamics). Keywords Psychotherapy processes Personality development State-trait dynamics Computer simulation Synergetics Mathematical modeling Computational systems psychology Introduction second sight both assumptions are everything but trivial. The fact that human development is a dynamic process There are some basic assumptions in psychotherapy which requires time series data in order to get an idea on what seem to be evident: psychotherapy is a process evolving in these processes look like. There is empirical evidence that time and psychotherapy intends to change personality. At doubts the linearity of human change processes and instead suggests discontinuity and nonlinearity (chaoticity) of the processes (Haken and Schiepek 2010; Hayes et al. 2007; & Helmut Scholler Kowalik et al. 1997; Lutz et al. 2013; Schiepek et al. firstname.lastname@example.org 1997, 2016a; Stiles et al. 2003; Strunk et al. 2015). In Gunter Schiepek consequence, the challenge for the development of theo- email@example.com retical models on change processes is to explain nonlinear dynamics and discontinuous pattern transitions. Acknowl- Institute of Synergetics and Psychotherapy Research, Paracelsus Medical University, Salzburg, Austria edging that the explanandum should be both, the outcome and the process, mathematical algorithms are required Department of Psychology, Ludwig Maximilians University, Munich, Germany which are able to create dynamics, e.g., computer simula- tions based on coupled nonlinear difference equations. University Hospital of Psychiatry, Psychotherapy, and Psychosomatics, Paracelsus Medical University, Salzburg, Conceptually, this approach of modeling change dynamics Austria is embedded in a meta-theoretical framework of nonlinear Department of Life Sciences and Chemistry, Jacobs dynamic systems and self-organization (Haken 2004; Gelo University, Bremen, Germany 123 442 Cognitive Neurodynamics (2018) 12:441–459 and Salvatore 2016; Haken and Schiepek 2010; Orsucci and traits—in other words: the development of personality. 2006, 2015; Pincus 2009; Salvatore and Tschacher 2012; The results we presented in previous publications focused Schiepek et al. 1992, 2016a; Strunk and Schiepek 2006). on the dynamics of the model, e.g., nonlinear features and The second assumption on personality development is deterministic chaos, and on the dependency of the dynamic just as challenging as the nonlinear dynamics conjecture. patterns (attractors) on the parameters—which can be The term ‘personality’ is a fuzzy psychological construct interpreted as traits (Schiepek et al. 2016b, 2017)—, but with different deﬁnitions, conceptualizations, and ways of did not consider the dynamic interaction between traits and operationalization. Early behavior therapists therefore states. Closing that gap is the aim of this article. neglected this construct and focused on observable (overt) behavior. In psychoanalysis, personality was part of the unconscious and its drive dynamics, based on early child- The model hood experiences and only partially accessible to conscious experience and reﬂection. In psychology, personality is This model takes for serious that one of the most robust usually deﬁned by traits in the sense of habitual patterns of ﬁndings in common factors research is the importance of behavior, thought, and emotion. According to this per- the client contributing to the course and outcome of psy- spective, traits are relatively stable over time, differ across chotherapy (Bohart and Tallman 2010; Duncan et al. 2004; individuals, and inﬂuence behavior. States, in contrast, are Orlinsky et al. 2004; Sparks and Duncan 2010; Wampold conceptualized as transitory and ﬂuctuating. The trait and Imel 2015). For this reason the model focuses on approach was based on Allport and Odbert’s work who psychological mechanisms which have repeatedly been clustered terms taken from an English dictionary that could shown to be important within the ‘‘client system’’ both be used to distinguish the behavior of one human being empirically and theoretically (e.g., Grawe 2004; Orlinsky from that of another (Allport 1937). They differentiated et al. 2004). Another reason for focusing on these variables between terms that represented general characteristics that is their correspondence to the factors (subscales) of the determine personality—consistent and stable modes of an Therapy Process Questionnaire (TPQ, Haken and Schiepek individual’s adjustment to his environment (traits)—and 2010), which is used in the routine practice of psy- terms that referred to temporary experiences, moods, and chotherapy feedback (Schiepek et al. 2016c). activities (states). Cattell (1943) distilled Allport and The model includes ﬁve variables which are connected Odbert’s trait terms into a useful taxonomy, and some by 16 functions, mediated by four parameters (Fig. 1). A decades later, the Big Five (Costa and McCrae 1992; detailed description of the constructs and the psychological Goldberg 1992) or the Big Six (Thalmayer et al. 2011) mechanisms were given in Schiepek et al. (2017) and will tried to capture the principal dimensions of human per- be explained in more detail in a book which currently is in sonality. Other models included the dynamics of person- preparation. For a better understanding, a short description ality development and the trans-situational variability of of the variables, parameters and functions will be given. human’s thinking, feeling, and behavior (Magnusson and Endler 1977; Mischel and Shoda 1995). For example, The variables Fleeson’s Whole Trait Model (Fleeson and Jayawickreme 2015) combines the evidence for interindividual differ- (E) Emotions. This is a bidimensional variable representing ences in average global traits with the evidence that people dysphoric emotions (e.g., anxiety, grief, shame, guilt, and also vary substantially around these averages. Conse- anger) at the upper end of the dimension (positive values of quently, they conceptualized personality traits as density E) and positive emotional experiences (e.g., joy, self-es- distributions of momentary states. Based on this model, teem, happiness) at the lower end (negative values of E). Wilson et al. (2016) tested, if ﬂuctuations in affect and/or This deﬁnition of polarity is based upon the results of a situational triggers account for ﬂuctuations in personality factor analysis of the Therapy Process Questionnaire (TPQ, states—measured in a sample of students by momentary Haken and Schiepek 2010), which is used to generate the ecological assessment—, ﬁnding that affect accounted for empirical data for model testing. most, but not all of the within-person variance of states. (P) Problem and stress intensity, symptom severity, Other than in the Fleeson approach, the model of psy- experienced conﬂicts or incongruence chotherapeutic change we refer to in this article (Schiepek (M) Motivation to change, readiness for the engagement et al. 2017) differentiates in a classical sense between traits in therapy-related activities and experiences and states. The intention of the model is to reproduce some (I) Insight; getting new perspectives on personal prob- basic features of psychotherapy dynamics, like the vari- lems, motivation, cognition, or behavior (clariﬁcation ability of states, the evolution of state dynamics, but also perspective in terms of Grawe 2004); confrontation with the evolution of traits and the interaction between states 123 Cognitive Neurodynamics (2018) 12:441–459 443 Fig. 1 The structure of the model illustrates the dependencies between the variables and the parameters of the system conﬂicts, avoided behaviors and cognitions, or with functions deﬁning the inﬂuence of other variables, that is, repressed traumatic experiences no arbitrary segmentations or thresholds have been intro- (S) Success, therapeutic progress, goal attainment, duced from the beginning. Thresholds and discontinuous conﬁdence in a successful therapy course. jumps of the dynamics are emerging from the dynamics and not forced by some speciﬁc preliminary assumptions. The parameters It should be noted that the variables and parameters are partially overlapping with the Research Domain Criteria The model includes four parameters which mediate the (RDoC; Insel et al. 2010), promoted by the National Institute interactions between variables. Depending on their values, of Mental Health, which address similar psychological the effect of one variable on another is intensiﬁed or constructs, e.g., ‘‘negative valence’’ (variable E) or ‘‘at- reduced, activated or inhibited. Formally they modify the tachment’’ (parameter a). Yet our model goes beyond the functions which deﬁne the relationship of the variables to RDoC list by connecting the constructs into a large-scale each other. model. Nonlinear dynamical models like the one proposed (a) Working alliance, capability to enter a trustful here are well suited to obtain this goal, not only by linking the cooperation with the therapist, quality of the therapeutic elements but rather by formulating mechanisms of their relationship, interpersonal trust. This parameter signiﬁes interaction producing the emerging dynamics. the disposition to engage in a trustful relationship (attach- An empirical validation of the model is in preparation ment disposition) and also resembles the realized quality of and will be based on 941 cases which were assessed (daily the therapeutic alliance self-ratings) by the process questionnaire TPQ during the (c) Cognitive competencies, capacities for mentalization last years. and emotion regulation, mental skills in self-reﬂection, and the level of the personality structure (in the sense of the The functions Operationalized Psychodynamic Diagnostics, www.opd- online.net) The shape of each function represents theoretical as well as (r) Behavioral resources or skills that are available for empirical ﬁndings from psychotherapy research (e.g., com- problem solving mon factors research) and other psychological topics like (m) Motivation to change as a trait, self-efﬁcacy, emotion regulation, motivation, problem-solving and self- hopefulness, reward expectation, and ‘‘health plan’’ as related cognition. The psychological interrelations between suggested by the control mastery theory (Silberschatz the variables were modelled by mathematical functions. 2009). Some connections are represented by functions of sigmoid The graphs in the coordinate planes of Fig. 2 illustrate shape and varying scales. The function EðÞ S ¼ t t1 how the shape of each function depends on the parameter 1:25 0:5 0:5m for example describes how negative 5S 0:5 1þe t1 values. The full range of the variables is covered by the 123 444 Cognitive Neurodynamics (2018) 12:441–459 Fig. 2 The ﬁgure represents the 16 functions of the model (for a Green function graphs correspond to the maximum of the respective detailed description see Schiepek et al. 2017). The variables noted on control parameter(s) (= 1), red graphs to the minimum of the the left of the matrix (lines) represent the input, the variables noted at parameter(s) (= 0). Blue graphs represent an in-between state the top (columns) represent the output. Each function is represented (0 \ parameter value \ 1) by a graph in a coordinate system (x-axis: input, y-axis: output). emotions E depend on therapeutic success S (Fig. 2, bottom on emotion regulation and the psychopathology of bor- left), i.e., the experience of negative emotions like fear, derline personality disorder (Fig. 2, left column, second grief, shame, or anger are reduced or are inversely related to from bottom). Increasing problems activate worrying and feelings of progress and being successful in solving personal distressing emotions. The more severe or stressing the problems, with a saturation effect for extreme values of S. problem, the more such emotions will be triggered (expo- The strength of the effect is mediated by parameter m,that nential increase). This emotion triggering effect is more is, by feelings of self-efﬁcacy and a general positive pronounced if the person has only minor competencies (red expectation in problem-solving efforts. The higher m,the line) in emotion-regulation, self-reﬂection, and mentaliza- better S will reduce worrying emotions. tion (parameter c) and/or reduced expectations in his/her Other relations, e.g., E(P) and M(P), required more capacity to solve problems or to manage difﬁcult or reﬁned mathematical functions to capture the psychologi- stressful situations (self-efﬁcacy expectation, parameter m). cal mechanisms. The dependence of negative emotions E With higher values of in c and/or m (green line), coping on the problem intensity P, for example, describes a strategies for the down-regulation of negative emotions at complex relationship and represents the state of knowledge distinct problem intensities will be available and can be 123 Cognitive Neurodynamics (2018) 12:441–459 445 applied. The higher c and/or m, the lower the maximum of made ﬁrst attempts to link psychological processes to E and the earlier coping mechanisms and emotion regula- underlying neuronal mechanisms. It is worth noticing that tion skills will reduce negative emotions. At low levels of he addressed the aim to link psychiatric disorders to the c and m (red line), even lower levels of affect intensities underlying neurobiological laws. More than a 100 years cannot be managed or reduced until completely distressing later, Kandel (1998) asked for a program on integration of and disturbing emotions (high levels of E) are interrupted, cognition and behavior (especially related to psychiatric repressed, or disconnected from conscious experience by phenomena) with biological ﬁndings on brain processes. consuming drugs or alcohol, by self-harm, or by mecha- Since his seminal paper, the ﬁeld developed rapidly and nisms of dissociation (switch of ego-states). studies using different brain imaging methods (e.g., fMRI, Finally, the functions are added to ﬁve coupled nonlin- EEG) revealed effects of psychotherapy on the activity of ear equations, one for each variable, determining the functional neuroanatomic structures and on neuronal net- dynamical system: works (for reviews see Barsaglini et al. 2014; Schiepek et al. 2011). Research also focused on the brain mecha- 1 1 EEðÞ ; I; P; S; c; r; m¼ c þ cþr 10E nisms involved in therapeutic change processes (Cozolino 20IðÞ 1 þ5 1 þ e 1 þ e 2010, 2015; Schiepek 2011). 1 cþm þ 0:5 þ 0:5 1 cþm 2þ3 1 P 2 ðÞ ðÞ 1þe Mathematical models were developed to explain the cþm cþm 25 1 P0:20:75 1 ðÞðÞ ðÞ 2 2 1 þ e neuronal mechanisms of speciﬁc disorders. For example, a 1:25 mechanistic framework of brain network dynamics underly- þ 0:5 0:5m 5S0:5 1 þ e ing Major Depressive Disorder (Ramirez-Mahaluf et al. 2015) described how abnormal glutamate and serotonin 1 1 IEðÞ ; M; S; a; c¼ þ metabolisms mediate the interaction of ventral anterior cin- aþc aþc 20E þ5 20M þ5 ðÞ ðÞ 2 2 1+ e 1+ e gulate cortex (vACC) and dorsolateral prefrontal cortex (dlPFC) to explain cognitive and affective symptoms and its 20jSjcþ5 1+ e medical treatment by Selective Serotonin Reuptake Inhibitors 1:261 (SSRI). Other approaches like The Virtual Brain (TVB; Leon MPðÞ ; S; r; m¼ ðÞ P0:050:85mðÞ 10:1þ19:9m 1 þ e et al. 2013; Ritter et al. 2013) integrate data from subjects (fMRI, MEG, or EEG) with full brain network simulations ðÞ P0:43þ0:03mðÞ 73m 1 þ e across different brain scales. TVB is a neuroinformatics 1 r þ m platform for network simulations using biologically realistic 5S 1 þ e 2 connectivity which allows for the reproduction of a broad range of dynamic features, e.g., focal or distributed changes 1 1:2 PEðÞ ; S; c; r¼ c þ 0:2 0:8r in the network dynamics of brain disorders and approaches to 10E 5S0:5 1+ e 1 þ e counteract those pathological processes. SEðÞ ; I; M; P; S; a; c; m; r Conceptually, simulations and measures at different 1:3 brain scales focus on physico-chemical mechanisms which ¼ 0:65 þ 0:35 ðÞ c þ m 1 5E0:5 1 þ e relate to mental or psychological phenomena (cognitions, 1 1 emotions) like statistical mechanics of gas dynamics relate þ þ ðaþmþrÞ ðaþmþrÞ 20I þ5 20M þ5 3 3 to phenomenological gas theory. In terms of Synergetics, 1+ e 1+ e 1 we deal with a relative micro level of a multi-level and aþmþr 20M 1 þ5 ðÞ multi-scale system which may create order parameters at 1+ e an emergent macro level (Haken 2002). Both levels are 1:25 c þ m þ 0:5 0:5 1 related to each other, but given our actual knowledge, there 5P0:5 1 þ e 2 exist emergent qualities at the macro level (e.g., phe- 1 m þ r þ þ 1 nomenological consciousness) which cannot be fully 10S 1+ e 2 reduced to the micro level. Anyway, the dynamics at two or more levels may be correlated (see the K model of Freeman 2000, 2004; Kozma 2016). In one of our own studies we Neural correlates of the phenomenological were able to show that order transitions in the dynamics of model cognitions and emotions during psychotherapy (assessed by daily self-ratings) were timely related to pattern tran- The variables and the parameters of this phenomenological sitions of brain activity (assessed by repeated fMRI scans; model are deﬁned at a psychological level, which of course Schiepek et al. 2013). is based on neuronal activity. Dating back to 1895, Freud 123 446 Cognitive Neurodynamics (2018) 12:441–459 A huge amount of neurophysiological studies investi- terms of Synergetics, the variables represent the order gated the neural underpinnings of the variables, parame- parameters of the system. Order parameters are variables ters, and also the mechanisms behind the functions of our which describe the global bottom-up dynamics of a complex model. Any attempt to delineate these ﬁndings would be system. They are constituted by many sub-systems or sub- beyond the scope of this article. Especially the neurobiol- processes (e.g., the amplitude and frequency of convection ogy of emotions (variable E) has created a neuro-psycho- cells in ﬂuid dynamics, which are constituted by the mole- logical subdiscipline of its own: affective neuroscience. cules of the ﬂuid), and also realize a top-down synchro- Also problem intensity (P) is related to the experience of nization, which regulates (orders) the dynamic behavior of stress and all neural and neuroendocrine mechanisms of the sub-systems or system components (enslaving principle) stress regulation (Subhani et al. 2018). (Haken 2004). Order parameters capture the most important Given the enormous amount of literature on the topic, information of a multi-component system on a few dimen- only some ﬁndings should illustrate that the parameters of sions (information compression). the model can be related to neuronal underpinnings. For While states correspond to the order parameters of the example, the neuronal mechanisms of emotion regulation, model, traits correspond to its control parameters. Psy- which is an important part of the parameter c, concern the chologically, the control parameters can be interpreted as top–down regulation of the dorsal and ventromedial pre- traits or dispositions changing at a slower time scale than frontal cortex and of the ACC on limbic structures, the variables or states (separation of the time scales). In including the insular cortex and the amygdalae as promi- terms of Synergetics, the change of control parameters nent regions (e.g., Etkin et al. 2015). Similar areas (e.g., the drives the phase transitions of the system (Haken 2004) (or dorsal and medial prefrontal cortex) seem to be involved in in a more general and psychological sense the order mentalization (for a review see Mahy et al. 2014), justi- transitions). Indeed, a linear and continuous change of one fying the combination of the two constructs in one or more parameters may have sustainable effects on the parameter (c). The neuronal correlates of the parameter dynamic patterns of a system, constituting a phase transi- m have been investigated by Hashimoto et al. (2015). tion (Haken 2004). The effect of a parameter shift in c is Based on the analysis of gray and white matter volumes, demonstrated in Fig. 3. A continuous shift (continuous the authors suggest an internal locus of control, associated stepwise increase) in the sensitive range of the parameter with self-regulation and reward expectation, encompassing produces a discontinuous jump of the system dynamics the anterior cingulate cortex, striatum, and anterior insula. (order to order transition, Haken and Schiepek 2010). Dopaminergic structures such as the ventral striatum (nu- However, there is a big difference between control cleus accumbens), the putamen or the nucleus caudatus, are parameters in physical or physiological experiments, which involved in reward expectation and motivation for goal are susceptible to direct external control (this is why they directed actions (Knutson et al. 2001; Hurano and Kawato are called control parameters), and psychological param- 2006). Krueger et al. (2007) found the paracingulate cortex eters in the sense of traits. Traits are merely indirectly open and the septal area involved in partnership building and to external input (Haken and Schiepek 2010). Traits in the maintenance of reciprocal trust, comparable to the client’s sense of skills or competencies can be developed, but not engagement in the therapeutic alliance (parameter a). The directly inﬂuenced. They are dependent on concrete modulation of neuronal activity by oxytocin and its behavior, emotions, and cognitions, that is, on the experi- receptor dynamics (Costa et al. 2009) relate to attachment ences a person has in numerous consecutive speciﬁc situ- styles as well as all neural networks recruited for empathy ations. Any training program for skills or competencies and theory of mind processes (Mahy et al. 2014) in inter- uses such an indirect way of actualization of behaviors, personal communication. These competencies together feelings, and thoughts, that is, by the way of states (e.g., with behavior skills for social interaction and problem experiencing new behavior). Learning or personality solving are concerned by the parameter r of our model. development can in that view be expressed as the modiﬁ- cation of the dynamics of a system by the modulation of the nonlinear functions that connect the order parameters with A synergetic interpretation of states each other (states), while these states in themselves can and traits modulate the traits or dispositions. There is a circular causality from traits to states and from states to traits, from The variables of the model can be understood as psycho- control parameters to the order parameter dynamics, and logical states with varying intensities with a sampling rate of from the dynamics of order parameters to control param- once per day, so that each iteration of a simulation run can be eters (Fig. 4). interpreted as a daily measurement of the variables. This Allowing for a short historical side note, the ﬁt of this corresponds to the way the TPQ is applied in practice. In conceptualization of personality development not only to 123 Cognitive Neurodynamics (2018) 12:441–459 447 Fig. 3 Order transition in the dynamics of the variable E. The mean level of E, at a lower frequency, and with higher amplitudes of numbers at the y-axis refer to the values of the parameter the chaotic oscillations. The attractors are shown below the time c (0 \ c \ 1, red line) and to the z-transformed values of E (blue series. For the generation of the attractors, the discrete iterations were line). The transition of the pattern depends on a stepwise linear splined by the Excel standard spline function. During the linear increase of the parameter c from 0.60 to 1.00 between iteration 100 stepwise increase of the control parameter, the transient attractor and 200. From iteration 0 to 100, the parameter is kept constant at combines features of the pre- and the post-attractor and by this is 0.60, creating a certain dynamic pattern (attractor). After the 200th more complex than each of both iteration, c is constant at 1.00, producing another pattern at a lower the emergence of patterns in perception, cognition, emo- tions, and behavior. In this paradigmatic frame, pattern formation is driven by basic psychological laws of ‘‘Gestalt’’. These ideas were expanded by Lewin (1936a, 1936b, 1951), who included the impact of human needs, social contexts, and the personality on behavior. His topological view on personality integrated the environment as it is perceived by a motivated subject. The environment as a gradient ﬁeld is given by the famous formula B = f (P, E): Behavior B is a function of the person P and his environment E. In this Lewinian tradition, the model pro- posed here is not aimed to describe averaged behavior for which statistics would be a suitable method, but focuses on the single case, that is, on the developmental trajectories of individual clients. Like in Lewin’s work, our model intends to explain psychological processes by mathematical means, Fig. 4 Circular causality between state (order parameter) and trait nowadays called computational systems psychology. (control parameter) dynamics. The feedback-loop includes different time-scales Model extension on parameter dynamics Synergetics but also to other concepts of self-organization in psychology should be remarked. Especially the Gestalt The circular causality between states and traits demands an psychology tradition goes back to the early twentieth extension of the state or order parameter model described century, when Gestalt psychologists Koehler so far, which is realized as coupled nonlinear difference (1920, 1940, 1947), Metzger (1940) and others described 123 448 Cognitive Neurodynamics (2018) 12:441–459 equations (discrete model with one equation for each parameter considering the differing time-scales by a variable, see Schiepek et al. 2017). The basic idea about the combination of averaging and weighting recent changes evolution of traits is its dependency on the increases or stronger than prior ones. Within a running window of decreases of the states, i.e., concrete experiences in emo- time length n (for the simulation runs of this paper, n = 14) the impact at t of the value depends on the sum tions (E), problem intensity (P), motivation to change (M), insight (I), and success (S). of all differences from the arithmetic mean of the Therefore, the functions describing the dynamics of the variable within the window, e.g., E E . Using parameters a, c, m and r depend on the values of these i¼1 variables. a depends on increases of success and on the this procedure, not the absolute level of the variable has experience of positive emotions. c depends on increased an effect, but its relative increases or decreases. In insight and on therapeutic success. Social and behavioral addition, we assume a memory effect which accentu- resources (r ) may also contribute to the evolution of c , since ates recent emotions or cognitions more than older t t these competencies may offer a broader range of personal ones. This is modeled by an exponential decay function experiences contributing to a better understanding of oneself with a characteristic steepness k from the latest value and of one’s social environment. In the opposite direction, within the running window (at t) to the oldest value at the evolution of r depends on cognitive competencies and on t–n. The exponential decay of the impact of each kðÞ tnþi skills in emotion regulation (c ), which allow for a more t variable on the parameter change is given by e . effective development of social and other behavioral skills, The ﬁlter functions for the variables are given by together with success in problem solving and therapeutic expressions like this (here illustrated by E): progress in other ﬁelds. The evolution of self-efﬁcacy, pos- itive reward expectation and a generalized hopeful attitude to kðÞ tnþi oneself (m ) depends on successful problem reduction, the t f ¼ d E E e ð5Þ E;t;n E tnþi t;n experience of positive emotions, increased state motivation i¼1 to change, and therapeutic success. In order to correct for the mean shift, which results The inﬂuence of the state variables on the progression of from using decay-affected difference-values within the the control parameters has to consider different time-scales running window, correction factors (d ,d , d , d , d ) E I M P S for the variables’ evolution on the one and the trait are introduced. Their values are d = d = d = d E P M I dynamics’ evolution on the other hand (see the ﬁlter = d = 0.535, for the decay-constants k they are cal- functions f in the parameter equations). Additionally, one culated from half-life constants s ¼ s ¼ s ¼ s ¼ E P M I has to prevent for favoring designated time-points, e.g., ln2 s ¼ 7d, using the relation k ¼ , resulting in distinct starting values. Therefore, the most important k ¼ k ¼ k ¼ k ¼ k ¼ 0:099. E P M I S effect on the parameters is exerted by the increase or • w , w , w , w are weights which are introduced in a c r m decrease of the state variables in relation to a decay-af- order to dampen the effect of the variables on the fected mean value, and the actual values a , c , r , m of the t t t t parameters, i.e., scaling them to an appropriate range parameters at time t are calculated by functions which respective to the variables. They model the sensitivity increase or reduce the parameter values of the last iteration and the impact of the state dynamics on the evolution of a , c , r , m to a certain amount—dependent on the t–1 t–1 t–1 t–1 the traits. For the simulation runs presented in this long term impact of variable dynamics: paper, w = w = w = w = 0.004167. a c r m • The constants 1/2, 1/3 and 1/4 normalize the sum of a ¼ a þ s w a f f ð1Þ t t1 a a t1 S;t;n E;t;n contributors of the ﬁlter functions (may it be variables or parameters) to 1. c ¼ c þ s w c f þ f þ r ð2Þ t t1 c c t1 I;t;n S;t;n t1 3 • The functions s ; s ; s ; s are saturation functions, a c m r which limit the growth or the reduction of the r ¼ r þ s w r f þ c ð3Þ t t1 r r t1 S;t;n t1 parameters onto the predeﬁned range from 0 to 1. For example, the saturation of the parameter c is realized by m ¼ m þ s w m t t1 m m t1 f f þ f þ f ð4Þ E;t;n P;t;n M;t;n S;t;n s ¼ k Dc 4 c 1 þ sgnðÞ Dc 1 sgnðÞ Dc Each equation consists of several elements that will now ðÞ c c þ ðÞ c c max t1 t1 min 2 2 be explained in detail: ð6Þ • f ,f ,f ,f ,f are ﬁlter functions which E,t,n P,t,n M,t,n I,t,n S,t,n represent the effect of each variable on the respective 123 Cognitive Neurodynamics (2018) 12:441–459 449 • k is a gain factor for a windowing procedure, which Results: model dynamics restricts the possible range of the parameters [0,1] to the range of complex or chaotic dynamics, as it In the following, some speciﬁc results of the simulated was deﬁned by inspection of the bifurcation system behavior are presented. The simulation dynamics diagrams of the system (see Fig. 6 in Schiepek which are shown in Figs. 5, 6, 7 and 8 represent some et al. 2017). For example, restricting c to the characteristic features of the system and of psychothera- interval 0:1 c 0:8 yields k ¼ c c ¼ 0:7. max min peutic processes. The dynamic patterns are based on • Dc is the difference between c and c . t–1 t speciﬁc parameter values and initial conditions, but can • The ﬁrst term within the bracket is activated only if also be generated by other simulation runs within a range there was an increase in c:if Dc [ 0 ? sgn(Dc)= of parameter values and seed keys. Even without any 1þsgnðÞ Dc speciﬁc interventions, unspeciﬁc dynamic noise applied to ? 1 ? ¼ 1. For a decrease Dc \ 0 ? 1þsgnðÞ Dc the variables can lead to a positive trend of the parameters sgn(Dc)=– 1 ? ¼ 0. With the same logic, (Fig. 5): a spontaneous transient period is realized at the the second term is activated (unequal to zero) if beginning, from high levels of E and P and low levels of S there was a decrease in the parameter. and M to a balanced dynamics of all variables. Evidently, • Furthermore, the saturation functions are activated without intensive or continuous stressors or bad experi- only if the parameter values are beyond a certain ences, the model is capable of realizing a trend, which in threshold, [ 0.8 or \ 0.2 for all parameters. Taken psychological terms might be interpreted as a personal c as an example: growth or self-actualization. On the long term, this could lead to spontaneous remission. ðÞ 1 c s jðc [ 0:8Þ\ðDc [ 0Þ Interventions, which were implemented between t =50 s ¼ s j0:2 c 0:8 ð7Þ c and t = 60 on all variables, have a time-limited impact on ðÞ c 1 s jðc\0:2Þ\ðDc\0Þ c the state dynamics and by this, also on the traits. However, an order transition is not triggered by these multiple • Concerning the evolution of the parameter a , the two interventions. aspects of parameter a can be taken into consideration. Punctual interventions are less likely to change attrac- As we noted above, this parameter signiﬁes the tors than continuous evolution. In the example of Fig. 6a, disposition to engage in a trustful relationship (attach- the interventions on S (? 38%) at t = 17, 30, and 50 have ment disposition). In the psychotherapy process, it also no impact on the dynamic pattern, and the parameters do refers to the empirically realized quality of the thera- not change neither except for small ﬂuctuations around a peutic relationship between patient and therapist. In stable state. However, longer periods of continuous inter- many studies, the therapeutic alliance has been proven vention—in Fig. 6b an intervention of ? 38% on S from as an important contributor to the therapeutic success t = 17 to 25 is applied—have a higher probability to (e.g., Flu¨ckiger et al. 2012; Wampold and Imel 2015). change patterns. The existence of bi- or multistability in the The alliance as perceived by the client can be measured dynamics of a system opens the option of order transitions by the items of the therapeutic alliance subscale of the with parameter drifts following the state dynamics, not TPQ. Hereby, the time series of the experienced quality only, as classical Synergetics predicts, from parameter of the therapeutic alliance of the psychotherapeutic drifts to order transitions. process is hereby available. The concrete value of the Interestingly, sometimes unspeciﬁc daily hassles or empirically given quality of the alliance at time t is spontaneous happiness, represented in the simulation as denoted b . The two aspects are combined by calculat- dynamic noise, can trigger order transitions. In Fig. 7a, a ing their mean, noise level of 10% on E and P and 5% on M, I and S has no long-term effect and qualitative impact on the dynamics (although from t = 35 to 45 a successful period occurs by a ¼ðÞ a þ b : ð8Þ t1 t chance). The same amount of noise, but with different random values, can trigger an order transition with long- Here, a is substituted by a ,the mean of a and b . t1 t1 t term consequences on the trait levels (Fig. 7b). Here—like If no information is available about the values of b ,they in Fig. 6b—the parameter drift seems to follow the state are set to b ¼ a and therewith a ¼ a in Eq. (8). t t1 t1 dynamics and to be a consequence, not a cause of the order transition. A closer look on the dynamics reveals a circular The interactive simulation system, performing simula- tion with the described framework and settings, can be used causality during the transition period: small changes in the on www.psysim.at. levels of the variables (here due to noise) increase the level 123 450 Cognitive Neurodynamics (2018) 12:441–459 Fig. 5 Noise-driven order transition between the 10th and the 20th z-transformed. For this and the following ﬁgures, the respective iteration, accompanied by an increase of all parameters. Between the simulations and simulation data are available for both download and 50th and the 60th iteration, a multiple intervention is introduced direct application with our online simulation tool PSYSIM (www. (? 20% on M, I, and S, - 20% on E and P). After this period, a psysim.at). We provide two types of links: with links named SIM-xx, spontaneous deterioration occurs since the effects of the interventions you can open our online simulation tool PSYSIM and load the input do not sustain. Parameters: a: red, m: green, c: bright blue, r: dark and output of the simulation applied to the actual ﬁgures for direct blue. Initial values: E: 97.6, P: 61.5, M: 7.5, I: 100, S: -40.7; all inspection and further processing. Result data can be downloaded in parameters: 0.30. Dynamic noise 30%, continuously. Variables: CSV formal by the links named CSV-xx. SIM-5, CSV-5 of the parameters, i.e., the client integrates new qualities of example of this simulation run, but also in many others (not his/her experience and continues with higher competencies. shown here), the model realizes a rebound effect to levels This in turn affects his/her experience, represented by lower than at start. In the long run, both—state- and trait- ‘‘better’’ values of the variables, until a new stable state is dynamics—evolve to patterns that entail improvement reached. From there, small perturbations (noise) cannot (recovery). shift the system any further; the variables and parameters Speciﬁc dynamics are shown when the b -vector, which ﬂuctuate around a certain ﬁx point. represents the empirically given dynamics of the thera- In many cases, a rebound effect occurs after a longer peutic alliance, is introduced. Figure 9 shows the effect of period of interventions. Correspondingly, many patients in interventions and of the alliance dynamics. The interven- real therapies indeed experience the release from inpatient tions start at t = 35, which realistically correspond to the treatment or from a day treatment center as a difﬁcult time. treatment onset in the day treatment setting of this speciﬁc Figure 8 illustrates this rebound effect: all interventions on client (diagnosis: obsessive–compulsive disorder). Until P, M, I and S are stopped at t = 100. Only a reducing effect that time, the client had not been involved in treatment on stressful emotions of -10% continues, what might programs because of holidays of the responsible therapist correspond to a continued intake of antidepressant or and of organizational problems at the ward. The client was anxiolytic drugs. The continued (e.g., pharmacological) disappointed, but from the moment the therapy started, she effect on E does not prevent the rebound effect to elevate developed a good therapeutic alliance with her therapists. the system to the same level and the same pattern as in the She was engaged in all treatments available to her, espe- beginning, before any intervention had been started. cially in a cognitive-behavioral therapy program. Moreover, it seems to prevent a self-organizing process which on the long term relaxes the dynamics on a different ‘‘healthy’’ attractor. But continuously and especially after the intervention on E was stopped, a positive development in success and on problem reduction takes place, corre- sponding to an increase in competencies of m and c. In the 123 Cognitive Neurodynamics (2018) 12:441–459 451 Fig. 6 a Punctual interventions on S (?38%) at t = 17, 30, 50. Data: Initial values of variables and parameters: E: 100, P: 79, M: 32.5, I: SIM-6a, CSV-6a. b Continuous interventions on S (? 38%) from 50, S: 33.5; a: 0.10, c: 0.35, r: 0.35, m: 0.10. Dynamic noise 10%, t = 27 to 25. Parameters: a: red, m: green, c: bright blue, r: dark blue. continuously. Variables: z-transformed. Data: SIM-6b, CSV-6b psychotherapy, this circular causality conceptualizes a Discussion model of personality development and exhibits important features of psychotherapy dynamics. In the described personality dynamics model of psy- chotherapy, a circular causality between traits and states Limitations was established. The dynamics of states—behavior, cog- nitions, and emotions of a client—can trigger order tran- There are some limitations in the current model and its sitions and modify the traits. This closed circle extends the mathematical realization. The model still contains a num- classical model of Synergetics, which focuses on the role of ber of parameters shaping the various inﬂuence functions, control parameters for the energy-driven destabilization of such that they conform to a wide range of empirical patterns (non-equilibrium phase transitions) onto a model knowledge about psychotherapy (see Schiepek et al. 2017). of interconnected order parameters (corresponding to In the long run, a more minimal model should be states) and control parameters (corresponding to traits). In 123 452 Cognitive Neurodynamics (2018) 12:441–459 Fig. 7 Two realizations (random numbers) of the same levels of 0.46, m: 0.53. Dynamic noise 10% on E and P, 5% on M, I, and S, dynamic noise (a, b). Parameters: a: red, m: green, c: bright blue, r: continuously. Variables: z-transformed. Data: SIM-7a, CSV-7a,b: dark blue. In both cases, the initial values of variables and parameters SIM-7b, CSV-7b are: E: 97.6, P: 61.5, M: 7.5, I: 100, S: - 40.7. a: 0.10, c: 0.75, r: constructed by understanding more deeply which model Questionnaire on a daily basis goes along with a process of elements are necessary and sufﬁcient for a particular internal inspection, where—formally speaking—the client dynamical behavior. maps his/her complex emotional pattern to certain values Another limitation concerns the question whether a of the variables. In this sense, the measurement process, model with continuous time (differential equations instead induced by the TPQ, forms these variables at discrete times of difference equations) will also have a chaotic regime. It and the psychotherapy dynamics as a system is periodically should be noted that the dimension of the model (D = 5) driven by the TPQ. It is well-known that such periodic would in principle allow for chaoticity also in continuous driving can trigger a complex dynamical response (Glass ¨ ¨ time. For the present investigation, we decided to explore 2001;Hutt 2001;Hutt et al. 2002). the discrete-time version of the model. Our argument here is that the dynamical variables indeed only exist at discrete time points. The process of ﬁlling out the Therapy Process 123 Cognitive Neurodynamics (2018) 12:441–459 453 Fig. 8 Interventions on E, P, and M start at t = 20, interventions on I increase slowly, and P decreases. It seems that a long-term recovery and S at t =25 (? 5% on M, ? 10% on S and I, - 10% on E and P). and self-healing process can only start if negative emotions are not Except for E, all interventions end at t = 100, the intervention on E suppressed, that is, the self-organizing effect onto another stable at- continues to t = 200. The interventions have an effect on all variables, tractor can only take place if the system can follow its own but also a distinct rebound effect in S and M (decreases) and P unrestricted dynamics. Initial values of variables and parameters: E: (increase) can be observed. The continued intervention on E (- 10%) 97.6, P: 61.5, M: 7.5, I: 100, S: - 40.7; a, c, r, m: 0.20. Dynamic until t = 200 reduces stressful emotions, but also the motivation to noise: 2%, continuously. Variables: z-transformed. Data: SIM-8, change (M) (upper part of the ﬁgure). After this period, M and S CSV-8 Other models of psychotherapy dynamics this model. One distinctive feature of the approach pre- sented in this paper compared to that of the Liebovitch– There are only few other attempts to mathematically model Peluso–Gottman et al. group is that the current approach focuses on the psychological processes of clients in relation psychotherapy. Peluso et al. (2012) and Liebovitch et al. (2011) focused on the co-evolution of emotional valences to their own experiences—not primarily on the client– therapist-interaction—and that we regard chaos and expressed by a therapist and his client. The differential equations deﬁned by the Liebovitch–Peluso–Gottman et al. chaoto-chaotic phase transitions as important features of group consist of segments of linear functions, each deﬁning psychotherapeutic processes (Schiepek et al. 2017). the gradient of emotional changes, which the client exerts In another mathematical analysis of psychotherapeutic on the therapist and vice versa. This leads to the prediction interventions (Haken and Tschacher 2017) the emergence of a pattern results from a competition of modes, each of stable ﬁx-point attractors of the therapeutic relationship at the intercept of the valence functions, or to drop-outs, having a parameter value attached. The model uses a speciﬁc connectionist system (the synergetic computer), depending on the initial conditions in the two-dimensional phase portrait. Chaos is not possible within the scope of which was designed as a mathematical tool for visual 123 454 Cognitive Neurodynamics (2018) 12:441–459 b Fig. 9 a Dynamics of the factor ‘‘Therapeutic Progress and Self- Conﬁdence’’ of the TPQ as it was assessed by daily self-ratings (corresponding to S) in the real client (t = 108 days) (left) and the simulated dynamics of S when interventions were added on P, M, and S from t = 35 to 100 (P: - 10%, M: ? 10%, S: ? 10%), and on E and I from t = 35to50(E: - 10%, I: ? 10%) (right). b Factor ‘‘Symptom Severity and Problem Intensity’’(P) of the TPQ, as empirically assessed in the real client (left) and simulated dynamics of P with the interventions as described in a (right). c Factor ‘‘Moti- vation to Change’’ (M) of the TPQ, as empirically assessed in the real client (left) and simulated dynamics of M with the interventions as described in a (right). d The dynamics of the factor ‘‘Therapeutic Alliance and Quality of the Therapeutic Relationship’’ of the TPQ as it was assessed in the real client (corresponding to the b vector) (left) and the evolution of the parameters a, c, r, m triggered by the dynamics of the variables and the interventions as described in a (right). Initial values of the variables and the parameters: E: 100; P: 79, M: 32.5, I: 50, S: 1; a = 0.10 (red), c = 0.60 (light blue), r = 0.35 (dark blue), m = 0.10 (green). Dynamic noise: 2% on E and P, 5% on M, I, S. Variables: z-transformed. Data: SIM-9, CSV-9, Patient Data: CSV-9P pattern recognition, assuming that the scenarios of psy- chopathology and therapeutic interventions are analogous to that of visual pattern recognition. This approach focuses on the question under which conditions a previously established psychopathological pattern will not be resti- tuted. One result of the simulation study is that successful corrective interventions should focus on one alternative pattern only. This alternative (healthy) pattern must be provided with higher valence (i.e., affective and motiva- tional intensity) than the pathological pattern. The authors interpret this ﬁnding as a support of an ‘‘holistic’’ rather than a symptom-focused treatment approach. It is prefer- able to intensively support a single alternative instead of many less and only partially supported alternative patterns with less motivational intensity than the disorder. Correc- tive intervention must be ‘‘valent’’, hence work with a focus on affective experiencing, emotion regulation, and motivation. Model testing In order to test the model proposed in this paper, the time series of 941 cases (\ 3% missing data in each case) are available from different psychotherapy centers, where therapy monitoring and therapy feedback by the TPQ has been implemented in routine practice for many years. A more speciﬁc empirical test on the state-trait-dynamics of the model is currently realized in the inpatient psy- chotherapy department of the Christian Doppler University Hospital, Salzburg, Austria. The prospective study intends to contribute to a better understanding of inter-individual variability of dynamic patterns corresponding to individual dispositions and competencies. The concrete dynamics of 123 Cognitive Neurodynamics (2018) 12:441–459 455 the variables, their initial values at the beginning of the Specific features and conclusions of our model therapeutic process, the daily input on E, I, M, P, and S as experienced by the client (interventions), and the parameter By summarizing the results and consequences of our levels of a, c, m, and r (pre and post treatment) of the mathematical model, some speciﬁc features—compared to clients, will be assessed. other models (see above)—become evident: As mentioned above, the variables of the model corre- • The option to create chaotic dynamics and chaoto- spond to ﬁve factors of the Therapy Process Questionnaire chaotic phase transitions (Kowalik et al. 1997)isan (Schiepek et al. 2016c), which is administered once per day important feature of change dynamics and corresponds in routine practice. The administration of the question- to empirical ﬁndings (Schiepek et al. 2016a, 2017). The naires is realized by an internet-based device, the Syner- model is designed in such a way that—depending on getic Navigation System (Schiepek et al. 2015, 2016a, c). the parameters—a spectrum of dynamic patterns (e.g., The parameters a, c, m, and r are widely used psycholog- chaotic patterns) occur. ical constructs, which can be assessed by known ques- • The model includes the quality of the therapeutic tionnaires: The parameter a is assessed by the ‘‘Adult relationship. Findings show that the therapeutic alli- Attachment Scale’’ (AAS, Schmidt et al. 2004) and the ance, as it is perceived by the client, correlates with and dynamics of the therapeutic relationship (the b vector of predicts the therapeutic outcome better than the alliance our model) by the Therapeutic Alliance Subscale of the as perceived by the therapist or an external observer TPQ. The parameter c is assessed by the ‘‘Hannover Self- (Horvath and Symonds 1991; Orlinsky et al. 2004). The Regulation Inventory’’ (a questionnaire on ego-functions model integrates the concrete empirical dynamics of the and competencies in self–regulation; Ja¨ger et al. 2012) and client-therapist-relationship of a speciﬁc case and takes by the ‘‘Emotionale–Kompetenz–Fragebogen’’ (Question- into consideration the evolution of the quality of naire on Emotional Skills; Rindermann 2009). The cooperation as perceived by the client. parameter r is assessed by the ‘‘Essen Inventory of • The model does not presume the existence of alterna- Resources’’ (Tagay et al. 2014). The parameter m is tive attractors or patterns in a potential landscape, but assessed by the ‘‘Beck Hopelessness Scale’’ (BHS; Beck explains how new attractors will emerge by modulating et al. 1974; Krampen 1994) with high scores in the BHS the parameters, which are shaping the landscape. In corresponding to low levels of m, and by the ‘‘Question- principle, there are two complementary kinds of naire on Optimistic Expectancies on one’s Competencies’’ interventions: First, interventions can be understood (Schwarzer 1994). as experimental inputs to explore the switching points Figure 10 illustrates how the model can be ﬁtted to the or to identify the triggers which may switch on a speciﬁc conditions of a client, if the empirical initial con- different attractor within the range of unique dynamic ditions, the interventions as assessed by the client, and patterns of the system. In the metaphor of potential ﬁnally the quality of the relationship to her fellow clients at landscapes, the ball (the realized system behavior) is the ward is taken into consideration for the simulation run. driven beyond the separatrix into another valley of the The empirical data and the simulation run refer to one of landscape—if it exists. Secondly, the interventions our study clients, diagnosed with posttraumatic stress dis- inﬂuence the parameters via the state dynamics, and the order combined with anorectic eating disorder. As can be parameters then reshape the landscape, creating new seen, the simulation run (b) with speciﬁc information on potential valleys (attractors). the client taken into consideration is more similar to the • There are many ways how to create change: All empirical process (c) than the simulation run without these variables (order parameters) of the model are open for additional information (e): there is a slow rhythm, but no interventions. Perhaps a converging effect of more than phase transition, and P and E are synchronized, whereas S one component—corresponding to more than one is antisynchronized. treatment approach—is preferred. This corresponds to the well-known Dodo-Bird effect, which implies that there are no substantial differences in the effectivity of treatments (e.g., Wampold and Imel 2015). • There might be a complementarity and synergistic effect of interventions, but without motivation to Here, instead of the subfactor ‘‘Quality of the therapeutic relation- change (M) and without a positively experienced ship’’ of the TPQ, the subfactor ‘‘Ward atmosphere and relationship to therapeutic bond, no dynamics of change will emerge. the fellow patients’’ was used as vector b in Eq. 8, since the latter has been proven to be even more important than the relationship to the Also, our model opens the way for an evolution of M professionals. This is also an example of how ﬂexible the model is in terms of testing alternative hypotheses. 123 456 Cognitive Neurodynamics (2018) 12:441–459 Fig. 10 Model test by using empirical data from a real client. a The variables from his environment. Below, c, d show the above time empirical time series of the variables E, P, and S as assessed by the series, but smoothed by an overlapping gliding window (window TPQ. b Simulation of the dynamics of E, P, and S with the width = 3, calculation of the arithmetic mean). In comparison to b, empirically assessed initial conditions, the b vector and the thera- e shows the simulation run without speciﬁcation of input and the b t t peutic interventions. The interventions for all variables were assessed vector. f Evolution of the parameters using the b vector. Variables: by the client’s daily ratings of the experienced input on these z-transformed motivation, or activation of symptoms (compare the and a (and of other states and traits) even when a client starts from bad initial conditions. ﬁndings of Geukes et al. 2017; Wilson et al. 2016). • A long-term stabilization of treatment effects requires a These patterns characterize the personality and evolve change in the levels of traits (control parameters), that in time by self-organizing processes. is, new or enhanced competencies and skills. Further developments on mathematical modeling and • There are long-term effects of psychotherapy, even data-related simulation of human change processes could after crises or rebound effects, which occur when open new ways of testing therapeutic interventions before treatments end or clients are released from inpatient or administering them on human beings. We do not expect other treatment settings. Psychological long-term any options for long term predictions in chaotic systems effects correspond to processes of neuronal reorgani- like this, but for short term predictions and early warning zation which also take time and have to be stabilized signs. Conceptually, the traits of the model could be related even in stressful environments. to the ego-functions and the levels of the personality • Crises in the sense of critical instabilities are concep- structure of clients as outlined by the Operationalized tualizable as important transients on the way to self- Psychodynamic Diagnostics (OPD, Doering et al. 2013). organized pattern transitions. The assessment of the traits (control parameters) of the • The model predicts inter- and intra-individual differ- model could be cross-validated by the semi-structured ences in context-speciﬁc behavior depending on traits interview procedures and the personality questionnaire and attractors. States ﬂuctuate depending on situational provided by the OPD. Finally, the phenomenological contexts (e.g., triggered by interventions) and on other (psychological) model could be more closely linked to the states. The interconnectedness of states and traits neural mechanisms of human change processes. Emergent implies that people react to situations or contexts by psychological mechanisms could be related to more basic personal patterns of cognitions, emotions, behavior, (meso- and micro-level) neural network dynamics (Bonzon 123 Cognitive Neurodynamics (2018) 12:441–459 457 Flu¨ckiger C, Del Re AC, Wampold BE, Symonds D, Horvath AO 2017; Freeman 2000; Haken 2004; Haken and Schiepek (2012) How central is the alliance in psychotherapy? a multilevel 2010; Kozma 2016) and by this, the promising approaches longitudinal meta-analysis. J Couns Psychol 59:10–17. https:// of computational systems neuroscience and computational doi.org/10.1037/a0025749 systems psychology could be integrated. 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